The present invention is generally related to surveying subterranean formations to facilitate recovery of natural resources, and more particularly to designing surveys and reducing the computational overhead associated with processing survey data.
Developments in numerical computation techniques have motivated research on Full-Waveform Inversion (FWI) approaches for geophysical applications. For example, R. G. Pratt, C. Shin, and G. J. Hicks, Gauss-newton and full newton methods in frequency-space seismic waveform inversion, Geophysical Journal International, 13, 341-362 (1998); C. Shin, K. Yoon, K. J. Marfurt, K. Park, D. Yang, H. Y. Lim, S. H. Chung, and S. Shin, Efficient calculation of a partial derivative wavefield using reciprocity for seismic imaging and inversion, Geophysics, 66, 1856-1863 (2001); A. Abubakar, P. van den Berg, and J. T. Fokkema, Towards non-linear inversion for characterization of timelapse phenomena through numerical modelling, Geophysical Prospecting, 51, 285-293 (2003); S. Operto, J. Virieux, P. Amestoy, J.-Y. L'Excellent, L. Giraud, and H. Ben-Hadj-Ali, 3D finite-difference frequency-domain modeling of visco-acoustic wave propagation using a massively parallel direct solver, A feasibility study: Geophysics, 72, SM195-SM211 (2007); D. Vigh, and E. W. Starr, 3D prestack plane-wave fullwaveform inversion, Geophysics, 73, VE135-VE144 (2008); W. Hu, A. Abubakar, and T. M. Habashy, Preconditioned non-linear conjugate gradient method for seismic full-waveform inversion, in Expanded Abstracts, U018, 71st EAGE Conference & Exhibition (June 2009); W. Hu, A. Abubakar, and T. M. Habashy, Simultaneous multifrequency inversion of fullwaveform seismic data, Geophysics, 74, R1-R14 (2009); Abubakar, W. Hu, T. M. Habashy, and P. M. van den Berg, Application of the finite-difference contrast-source inversion algorithm to seismic full-waveform data, Geophysics, 74, WCC163-WCC174 (2009). FWI seismic inversion generally deals with processing a large size data set, which tends to be a processing bottleneck. A large number of sources in the survey contributes to a large computational cost in running the forward simulator a number of times corresponding to the number of sources. A large number of receivers contributes to the computational cost of constructing the sensitivity (Jacobian) matrix as well as in inverting the Hessian matrix in a gradient-type inversion approach. Recently a simultaneous-source encoded FWI approach has been proposed to reduce the number of sources used in the inversion, see H. Ben-Hadj-Ali, S. Operto, and J. Virieux, Efficient 3d frequency-domain full waveform inversion (fwi) with phase encoding, in Expanded Abstracts, P004, 71st EAGE Conference & Exhibition (2009); F. J. Herrmann, Y. Erlangga, and T. T. Y. Lin, Compressive sensing applied to fullwave form inversion, in Expanded Abstracts, 5016, 71st EAGE Conference & Exhibition (2009); J. Krebs, J. Anderson, D. Hinkley, R. Neelamani, S. Lee, A. Baumstein, and M. D. Lacasse, Fast full-wavefield seismic inversion using encoded sources Geophysics (2009). In this approach a large number of physical sources are converted into one simultaneous source or several simultaneous sources by summing up the individual physical sources using a phase encoding technique (see S. A. Morton, and C. C. Ober, Faster shot-record depth migrations using phase encoding, in Expanded Abstracts, 1131-1134, SEG Annual Meeting (1998)). This phase encoding technique has also been applied for the prestack migration as in L. A. Romero, D. C. Ghiglia, C. C. Ober, and S. A. Morton, Phase encoding of shot records in prestack migration, Geophysics (2000). It has been pointed out that this approach is more sensitive to noise than the standard FWI method. J. Krebs, J. Anderson, D. Hinkley, R. Neelamani, S. Lee, A. Baumstein, and M. D. Lacasse, Fast full-wavefield seismic inversion using encoded sources Geophysics (2009) attempted to reduce this noise problem by changing the encoding scheme that is used in the inversion in each inversion iteration. However, this results in the increase number of iterations needed by the simultaneous-source encoded FWI approach. Several techniques for estimating a subsurface electromagnetic model by iteratively minimizing the difference between observed and simulated data are described in T. M. Habashy and A. Abubakar, A general framework for constrained minimization for the inversion of electromagnetic measurements, Progress in Electromagnetics Research, PIER 46, pp. 265-312, (2004) and the references therein.